Positivity with Long-Range Interactions

TL;DR

The paper develops infrared-finite, analytic amplitudes that incorporate long-range interactions, enabling the derivation of positivity bounds in effective field theories with electromagnetic and gravitational forces.

Contribution

It introduces a new class of amplitudes satisfying key physical properties, allowing positivity bounds to be applied in theories with long-range forces in four dimensions.

Findings

Explicit positivity bounds for pion-electromagnetism-gravity interactions.

Amplitudes reproduce infrared-finite inclusive cross sections.

Framework applicable to effective field theories with long-range interactions.

Abstract

We introduce infrared finite, analytic, crossing symmetric, Regge behaved, and Lorentz invariant amplitudes $\mathcal{M}_{\mathcal {E}}$, labeled by the experimental energy resolution $\mathcal{E}$ for detecting soft photons and gravitons. For $\mathcal{E}$ exponentially smaller than any hard scale, they also satisfy unitarity and their associated cross sections reproduce the inclusive, infrared-finite cross sections of ordinary amplitudes. These properties make $\mathcal{M}_{\mathcal{E}}$ suitable for deriving infrared-safe positivity bounds on effective field theories in the presence of long-range forces even in $D=4$. As an illustration, we present explicit bounds in the low-energy theory of pions coupled to electromagnetism and gravity.